title: Tensorial Minkowski functionals of triply periodic minimal surfaces.
abstract: A fundamental understanding of the formation and properties of a complex spatial structure relies on robust quantitative tools to characterize morphology. A systematic approach to the characterization of average properties of anisotropic complex interfacial geometries is provided by integral geometry which furnishes a family of morphological descriptors known as tensorial Minkowski functionals. These functionals are curvature-weighted integrals of tensor products of position vectors and surface normal vectors over the interfacial surface. We here demonstrate their use by application to non-cubic triply periodic minimal surface model geometries, whose Weierstrass parametrizations allow for accurate numerical computation of the Minkowski tensors.
authors.affiliation: Institut für Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, 91058 Erlangen, Germany ; Karlsruhe Institute of Technology, Institut für Stochastik, Kaiserstrasse 89, 76128 Karlsruhe, Germany.
authors.forename: Walter
authors.initials: W
authors.lastname: Mickel
authors.forename: Gerd E
authors.initials: GE
authors.lastname: Schröder-Turk
authors.forename: Klaus
authors.initials: K
authors.lastname: Mecke
keywords: anisotropy; integral geometry; lipid self-assembly; minimal surface; morphology; porous material